Global optimal vaccination in the SIR model: properties of the value function and application to cost-effectiveness analysis

Mathematical Biosciences
Laetitia Laguzet, Gabriel Turinici

Abstract

This work focuses on optimal vaccination policies for an Susceptible-Infected-Recovered (SIR) model; the impact of the disease is minimized with respect to the vaccination strategy. The problem is formulated as an optimal control problem and we show that the value function is the unique viscosity solution of an Hamilton-Jacobi-Bellman (HJB) equation. This allows to find the best vaccination policy. At odds with existing literature, it is seen that the value function is not always smooth (sometimes only Lipschitz) and the optimal vaccination policies are not unique. Moreover we rigorously analyze the situation when vaccination can be modeled as instantaneous (with respect to the time evolution of the epidemic) and identify the global optimum solutions. Numerical applications illustrate the theoretical results. In addition the pertussis vaccination in adults is considered from two perspectives: first the maximization of DALY averted in presence of vaccine side-effects; then the impact of the herd immunity on the cost-effectiveness analysis is discussed on a concrete example.

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Citations

Apr 7, 2016·Journal of Mathematical Biology·Paulo DoutorFabio A C C Chalub
Nov 6, 2018·Journal of Mathematical Biology·Bruno BuonomoAlberto d'Onofrio
Jul 31, 2018·Mathematical Medicine and Biology : a Journal of the IMA·Bruno BuonomoAlberto d'Onofrio
Mar 9, 2021·Journal of Optimization Theory and Applications·Pierre-Alexandre BlimanNicolas Vauchelet
Aug 3, 2021·Applied Mathematics and Optimization·Emanuel Javier FerreyraJuan Pablo Pinasco
Aug 16, 2021·Computer Methods and Programs in Biomedicine·Regina PadmanabhanMohammed Abdulla Al-Hitmi

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